Spectral density estimation is a widely studied subject in the field of signal processing, and we will rely on classical techniques provided there [1]}, [2]}, [3]}.
In particular, the periodogram is a standard estimate of the density function \(f_\zeta \)  of an absolutely continuous spectral measure \(\zeta \) , often also referred to as power spectral density.
When the spectral measure of a signal is purely discrete, i.e. the signal is produced by sinusoidal waves alone, the periodogram still proves to be a powerful tool for the estimation of frequencies [3]}.
Such a sinusoidal signal \(X=\left\lbrace X(t):t\in \mathbb {R}\right\rbrace \)  is modeled by
\(X(t)=\mu +\sum \limits _{k=1}^\infty r_k\cos \left(\phi _k+\lambda _kt\right)+Y(t),\) 
